Left Hand-Right Hand Solving Systems of Equations

In this lesson, students gather data, plot points, graph lines and develop a conceptual understanding of the three different types of possible solutions to a system of two equations with two unknowns. In this lesson, students gather data, plot points, graph lines and develop a conceptual understanding of the three different types of possible solutions to a system of two equations with two unknowns.

Standards & Objectives

CCSS.Math.Content.6.SP.B.5
Summarize numerical data sets in relation to their context, such as by:
CCSS.Math.Content.7.EE.B.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by...
CCSS.Math.Content.7.RP.A.2
Recognize and represent proportional relationships between quantities.
CCSS.Math.Content.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships...
CCSS.Math.Content.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive...
CCSS.Math.Content.8.EE.C.7
Solve linear equations in one variable.
CCSS.Math.Content.8.EE.C.8
Analyze and solve pairs of simultaneous linear equations.
CCSS.Math.Content.8.F.A.1
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting...
CCSS.Math.Content.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal...
CCSS.Math.Content.8.F.A.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For...
CCSS.Math.Content.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a...
CCSS.Math.Content.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or...
CCSS.Math.Content.8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe...
CCSS.Math.Content.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For...
GLE 0401.1.3
Demonstrate knowledge of Standard English sentence structure.
GLE 0506.5.2
Describe the shape and important features of a set of data using the measures of central tendency.
GLE 0606.3.1
Write and solve two-step equations and inequalities.
GLE 0606.3.2
Interpret and represent algebraic relationships with variables in expressions, simple equations and inequalities.
GLE 0606.3.3
Extend order of operations to include grouping symbols and exponents.
GLE 0606.3.5
Use multiple representations including symbolic algebra to model and/or solve contextual problems that involve linear relationships.
GLE 0706.2.3
Develop an understanding of and apply proportionality.
GLE 0706.3.2
Understand and compare various representations of relations and functions.
GLE 0706.3.3
Understand the concept of function as a rule that assigns to a given input one and only one number (the output).
GLE 0706.3.5
Understand and graph proportional relationships.
GLE 0706.3.6
Conceptualize the meanings of slope using various interpretations, representations, and contexts.
GLE 0706.3.7
Use mathematical models involving linear equations to analyze real-world phenomena.
GLE 0706.3.8
Use a variety of strategies to efficiently solve linear equations and inequalities.
GLE 0806.3.2
Represent, analyze, and solve problems involving linear equations and inequalities in one and two variables.
GLE 0806.3.3
Solve systems of linear equations in two variables.
GLE 0806.3.4
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
GLE 0806.3.5
Use slope to analyze situations and solve problems.
GLE 0806.5.2
Select, create, and use appropriate graphical representations of data (including scatterplots with lines of best fit) to make and test conjectures.
SPI 0606.3.2
Use order of operations and parentheses to simplify expressions and solve problems.
SPI 0606.3.8
Select the qualitative graph that models a contextual situation (e.g., water filling then draining from a bathtub).
SPI 0706.1.3
Recognize whether information given in a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.
SPI 0706.3.2
Determine whether a relation (represented in various ways) is a function.
SPI 0706.3.3
Given a table of inputs x and outputs f(x), identify the function rule and continue the pattern.
SPI 0706.3.4
Interpret the slope of a line as a unit rate given the graph of a proportional relationship.
SPI 0706.3.5
Represent proportional relationships with equations, tables and graphs.
SPI 0706.3.6
Solve linear equations with rational coefficients symbolically or graphically.
SPI 0706.3.7
Translate between verbal and symbolic representations of real-world phenomena involving linear equations.
SPI 0706.3.8
Solve contextual problems involving two-step linear equations.
SPI 0706.3.9
Solve linear inequalities in one variable with rational coefficients symbolically or graphically.
SPI 0806.1.2
Interpret a qualitative graph representing a contextual situation.
SPI 0806.1.3
Calculates rates involving cost per unit to determine the best buy.
SPI 0806.3.1
Find solutions to systems of two linear equations in two variables.
SPI 0806.3.2
Solve the linear equation f(x) = g(x).
SPI 0806.3.4
Translate between various representations of a linear function.
SPI 0806.3.5
Determine the slope of a line from an equation, two given points, a table or a graph.
SPI 0806.3.6
Analyze the graph of a linear function to find solutions and intercepts.
SPI 0806.3.7
Identify, compare and contrast functions as linear or nonlinear.
SPI 0806.5.3
Generalize the relationship between two sets of data using scatterplots and lines of best fit.
TSS.Math.6.SP.B.5
Summarize numerical data sets in relation to their context.
TSS.Math.7.EE.B.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by...
TSS.Math.7.RP.A.2
Recognize and represent proportional relationships between quantities.
TSS.Math.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in...
TSS.Math.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and derive...
TSS.Math.8.EE.C.7
Solve linear equations in one variable.
TSS.Math.8.EE.C.8
Analyze and solve systems of two linear equations.
TSS.Math.8.F.A.1
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an...
TSS.Math.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
TSS.Math.8.F.A.3
Know and interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
TSS.Math.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description...
TSS.Math.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear...
TSS.Math.8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such...
TSS.Math.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a...

Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.

Learning objectives:

Learning Objectives:

Students will be able to:

• Create scatterplots for two sets of data and find the equation of a line of best fit for both sets of data.
• Determine the three different types of possible solutions to a system of two equations with two unknowns.
• Interpret the meaning of the intersection of two lines as a solution to a system of equations.

Lesson Variations

Blooms taxonomy level:
Understanding